A141964 -id:A141964 - cp's OEIS frontend

A141963 Primes congruent to 23 mod 27.

23, 131, 239, 293, 347, 401, 509, 563, 617, 887, 941, 1049, 1103, 1319, 1373, 1427, 1481, 1697, 1913, 2129, 2237, 2399, 2777, 2939, 3209, 3371, 3533, 3803, 3911, 4019, 4073, 4127, 4289, 4397, 4451, 4721, 4937, 5099, 5153, 5261, 5477, 5531, 5639, 5693, 5801

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A141964, A141965.

[p: p in PrimesUpTo(7000) | p mod 27 eq 23 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[23, 30000, 27], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jun 21 2011 *)

is(n)=isprime(n) && n%27==23 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 18n log n. - Charles R Greathouse IV, Jul 02 2016

A380474 Numbers k such that A380459(k) has no divisors of the form p^p, while A003415(k) has such a divisor or is 0.

Original entry on oeis.org

1, 158, 482, 698, 914, 1238, 1346, 1454, 1994, 2102, 2426, 2642, 2858, 2966, 3398, 3506, 3722, 4262, 4478, 4586, 4694, 5234, 5342, 5666, 5774, 6098, 6638, 6746, 7286, 7394, 7934, 8042, 8258, 9014, 9122, 9446, 9662, 9986, 10202, 10418, 10958, 11282, 11498, 11714, 12146, 12686, 12794, 12902

Offset: 1

Antti Karttunen, Feb 02 2025

nonn

Because all terms k of A380468 are squarefree, they are also in A048103, so A003415(k) is outside of A048103 only if k is in A327934 or k = 1.
Like A380478, also this (after the initial 1) is a subsequence of A039956. The first three terms k with A001222(k) > 2 are: 11362082, 16782482, 20965982.
Contains 2*A141964 as a subsequence, because all primes p congruent to 25 mod 27 are also congruent to 1 mod 6, therefore A276086(p) is a nonmultiple of 3 in those cases and thus coprime with A276086(2) = 3.
In contrast, neither all 2*(primes congruent to 3123 mod 3125) nor all 2*(primes congruent to (7^7)-2 mod 7^7, like 1647082) are present. The missing ones are those for which A276086(p) is a multiple of 9, i.e., when p is in A047257.

Antti Karttunen, Table of n, a(n) for n = 1..20000
Index entries for sequences related to primorial base.

Cf. A003415, A047257, A048103, A141964, A276086, A358215, A380459.
Intersection of A380468 and ({1} U A327929), or equally of A380478 and ({1} U A327934).
After initial 1, a subsequence of A039956.

is_A380474(n) = (A380467(n) && !A368915(n));

A141960 Primes congruent to 19 mod 27.

Original entry on oeis.org

19, 73, 127, 181, 397, 613, 829, 883, 937, 991, 1153, 1423, 1531, 1693, 1747, 1801, 2017, 2179, 2287, 2341, 2503, 2557, 2719, 3259, 3313, 3529, 3583, 3637, 3691, 3853, 3907, 4177, 4231, 4339, 4447, 4663, 4933, 4987, 5419, 5527, 5581, 5689, 5743, 5851, 6067

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A141963, A141964, A141965.

[p: p in PrimesUpTo(7000) | p mod 27 eq 19 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[19, 30000, 27], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jun 21 2011 *)

is(n)=isprime(n) && n%27==19 \\ Charles R Greathouse IV, Jul 03 2016

a(n) ~ 18n log n. - Charles R Greathouse IV, Jul 03 2016

A141962 Primes congruent to 22 mod 27.

Original entry on oeis.org

103, 157, 211, 373, 643, 751, 859, 967, 1021, 1129, 1237, 1291, 1399, 1453, 1669, 1723, 1777, 1831, 1993, 2371, 2749, 2803, 2857, 3019, 3181, 3343, 3559, 3613, 4099, 4153, 4261, 4423, 4639, 4801, 4909, 5179, 5233, 5449, 5503, 5557, 5827, 5881, 6043, 6151

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A141964, A141965.

[p: p in PrimesUpTo(7000) | p mod 27 eq 22 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[22, 30000, 27], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jun 21 2011 *)

is(n)=isprime(n) && n%27==22 \\ Charles R Greathouse IV, Jul 03 2016

a(n) ~ 18n log n. - Charles R Greathouse IV, Jul 03 2016

cp's OEIS Frontend

A141963 Primes congruent to 23 mod 27.

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A380474 Numbers k such that A380459(k) has no divisors of the form p^p, while A003415(k) has such a divisor or is 0.

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A141960 Primes congruent to 19 mod 27.

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A141962 Primes congruent to 22 mod 27.

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